I Higgs particle vs. Higgs field

Does it make sense to say that the Higgs boson is an excitation in the Higgs field in much the same way that a fermion such as an electron is an excitation in the electromagnetic field? I am trying to understand the difference between the Higgs field, which is everywhere, and the Higgs boson which we only see under conditions of extremely energetic particle collisions.

I think the important thing to know is that the vev of the Higgs field provides the masses of the gauge bosons and fermions in the standard model. The symmetries constrain the form of the Higgs field, and it is only after counting that one concludes that (with one Higgs field) not all the degrees of freedom are used to generate mass-terms. This results in one Higgs particle.

I'm not sure how, but I think you could imagine a model in which ALL the degrees of freedom of the Higgs field are used to generate mass terms, with no dynamical dof's left. In that case no Higgs particle would manifest itself to us.

I'm not sure how, but I think you could imagine a model in which ALL the degrees of freedom of the Higgs field are used to generate mass terms, with no dynamical dof's left. In that case no Higgs particle would manifest itself to us.

yes I thin... if you would have been too much into it and had broken the [itex]U_{Q}(1)[/itex]...

First, it is impossible for fermion fields to have a large constant non-zero average value in nature. This is related to the difference between fermions and bosons; bosons can be non-zero on average, but fermions really can’t. So we can forget about electrons (and their cousins the muons and the taus), about neutrinos, and about the quarks. Fermions can pair with each other or with anti-fermions to make composite bosons, and those composite bosons can be non-zero on average. In fact this is true of the up and down quarks and their antiquarks, and it is true of electrons in a superconductor. But that’s a long story, and not our immediate concern.

What about the photon field, the gluon field, the W and the Z field? These are all bosons. In principle these fields could have a constant non-zero value on average throughout the universe. It is experiment, not theory, that says this isn’t the case. A large non-zero value for the electric field would have all sorts of effects that we do not observe, including most significantly an apparent violation of rotational invariance at large distance scales. The electric field is a vector (spin-1) — it points in a particular direction — so if it were non-zero, the direction in which its non-zero value points would be different from the other directions.